Please help me on this 4 set theory, I have start by drawing the 4 circles and put 3 at the center and 5 outside of the circles but I don't know the pattern to input the other values.
52—watched Football
56—watched Basketball
62—watched Tennis
60—watched Golf
19—watched Football and Tennis
21—watched Football and Basketball
20—watched Basketball and Tennis
27—watched Football and Golf
30—watched Basketball and Golf
21—watched Tennis and Golf
3—watched Football, Basketball and Tennis
15—watched Football, Basketball and Golf
10—watched Football, Tennis and Golf
10—watched Basketball, Tennis and Golf
3—watched all four of these sports
5—Don't watched any of these four sports.
Use a venn diagram to answer each question
(a) How many of these viewers watched Football, Basketball and Tennis but not Golf
(b) How many watched exactly one of these sport
(c) How many watched exactly two of these four sport?
Cannot draw venn diagram on these posts.
To solve this problem using the Venn diagram, we can systematically fill in the values given by the statements.
Step 1: Draw four circles representing Football, Basketball, Tennis, and Golf.
Step 2: Write the values given in the statement inside or outside the circles accordingly.
52—watched Football
56—watched Basketball
62—watched Tennis
60—watched Golf
19—watched Football and Tennis
21—watched Football and Basketball
20—watched Basketball and Tennis
27—watched Football and Golf
30—watched Basketball and Golf
21—watched Tennis and Golf
3—watched Football, Basketball and Tennis
15—watched Football, Basketball and Golf
10—watched Football, Tennis and Golf
10—watched Basketball, Tennis and Golf
3—watched all four of these sports
5—Didn't watch any of these four sports.
Step 3: To find the answer to each question:
(a) How many of these viewers watched Football, Basketball, and Tennis but not Golf?
To find this, look for the value that represents the intersection of Football, Basketball, and Tennis (3) and subtract the value for Football, Basketball, Tennis, and Golf (which is given as 0). Hence, the answer is 3 - 0 = 3 viewers.
(b) How many watched exactly one of these sports?
To find this, add up the values for each circle that contain only one value (Football only, Basketball only, Tennis only, or Golf only). Summing up these values, we get 52 + 56 + 62 + 60 = 230 viewers.
(c) How many watched exactly two of these four sports?
To find this, add up the values for each possible intersection of two circles (e.g., Football and Basketball only, Football and Tennis only, etc.). Summing up these values, we get 19 + 21 + 20 + 27 + 30 + 21 = 138 viewers.
So, the final answers are:
(a) 3 viewers watched Football, Basketball, and Tennis but not Golf.
(b) 230 viewers watched exactly one of these sports.
(c) 138 viewers watched exactly two of these four sports.